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We are asked to find the equation of a line that passes through the points \((-4, -6)\) and \((8, -6)\).

### Step 1: Find the slope
The formula for the slope \(m\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Substitute the points \((-4, -6)\) and \((8, -6)\):

\[
m = \frac{-6 - (-6)}{8 - (-4)} = \frac{0}{12} = 0
\]

Since the slope is 0, the line is horizontal.

### Step 2: Write the equation of the line
A horizontal line has the equation \(y = b\), where \(b\) is the constant \(y\)-coordinate of any point on the line. Since both points have \(y = -6\), the equation of the line is:

\[
y = -6
\]

Thus, the equation of the line is \(y = -6\).

Would you like further details or explanations?

Here are five related questions for practice:
1. What is the slope of a vertical line?
2. How do you find the equation of a line given the slope and a point?
3. What is the slope of the line passing through \((3, 4)\) and \((3, 7)\)?
4. Can a line have an undefined slope? If yes, what does it mean?
5. How do you convert a line equation from point-slope form to slope-intercept form?

**Tip**: Horizontal lines always have a slope of 0, while vertical lines have undefined slopes!

What is an equation of the line that passes through the points (-4, -6) and (8, -6)?

Learn how to find the equation of a horizontal line passing through the points (-4, -6) and (8, -6). This step-by-step solution explains key concepts like the slope of a line and how to write the equation for horizontal lines. Perfect for students in Grades 8-10.

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